A follow-on point is that figures in an appraisal should in no way be loaded by the existence of provisions or contingencies. In fact, the inclusion of a provision or contingency is quite fatuous. No moneys have been committed - this is just the appraisal stage. It is the most likely outcome that should be appraised for sensitivity. It is also arguable that there is no need for provisions on sanctioned projects - if they exist they will only be used!

However, when carrying out the sensitivity analysis, risks may become evident. The need for and amount of provisions, should the project be sanctioned, may well be capable of quantification. A business then may set up specific provisions for specific projects or may wish to hold central provisions as part of its risk management process or simply for political reasons.

'One at a time' approach

This method looks at changes in all parameters, or at least those considered the most critical (sensitive), one at a time; for example, if selling price is considered the most critical parameter, what decrease from the expected sales can be tolerated before the project is not viable - that is, NPV is down to zero?

TABLE 11.13'One at a time' sensitivity analysis

Again using a basic model with detail showing sales inflows and operating cost outflows rather than just the net inflows, a 'one at a time' sensitivity analysis may be carried out (Table 11.13).

The question is how to determine and demonstrate in an intelligible manner the effect of changes in the parameters (estimates of cash flow) on the outcome - the amount of the NPV. A simple and thus intelligible method of doing this is to express (in terms of percentage) the adverse change in an expected cash flow which may be tolerated, or in other words, to demonstrate the maximum unfavourable change in a parameter as a percentage of the original estimate of the parameter. The maximum tolerable or unfavourable change which can be accepted is where the NPV becomes zero. In the example above, a decrease of NPV of 10,786 can be tolerated. This present amount can then be related to adverse changes in the parameters one at a time.

For example: by how much could the estimate of cost of the investment rise without the project being rejected?

For NPV to be zero, investment cost would have to rise by the amount of the NPV, 10,786, to 24,786, which is 77.04 per cent more than the expected cost.

The question can then be asked: is the estimate of original capital costs at all likely to be 77 per cent out? If so (!!), and this risk cannot be managed, this project should quite clearly be rejected.

Sensitivity analysis is most easily carried out with the use of spreadsheets or specialist software. Either by using 'trial and error', using the 'goal seek' function or devising suitable formulae, it is possible to quickly review the maximum tolerable changes of all of the parameters one at a time.

Table 11.14 shows the spreadsheet reworked to give zero NPV as the initial investment has been increased by 77.04 per cent.

TABLE 11.14 The spreadsheet reworked to give zero NPV

In Table 11.15 the sales are reworked, showing that a reduction of 7.53 per cent results in zero NPV.

TABLE 11.15 Sales reworked

The example goes on to show how the other parameters may be tested for sensitivity one at a time. A table of the results gives a useful overall guide to the sensitivity of the project. In the example above, the table of the three sensitive parameters has been compiled by trial and error and shows that with a fall in sales of 17.85 per cent, the NPV is zero (Table 11.16). An important, obvious point is that the larger the parameter the more sensitive it will be. In this example, cash in - the sales - is almost twice the cash out, therefore any percentage change in cash in has almost twice the effect of an equal percentage change in cash out.

TABLE 11.16 The sensitivities identified by trial and error - example for payroll

Linked parameters

If two or more parameters are inextricably linked, a 'one at a time' analysis may still be carried out. The linked parameters can be reviewed together through likely ranges.

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